Agriculture Reference
In-Depth Information
for the parameter
θ
.
u
1
and
u
2
are known as
H
0
:
μ ¼ μ
0
,
(1)
μ 6¼ μ
0
,
(2)
μ > μ
0
, and
confidence limits and 1
α
is called the confi-
(3)
μ < μ
0
are the alternative hypotheses.
In testing of hypothesis, a
dence coefficient.
is a
function of sample observations whose computed
value when compared with the probability distri-
bution, it follows, leads us to take final decision
with regard to acceptance or rejection of null
hypothesis.
test statistic
9.2
Testing of Hypothesis
A statistical hypothesis
is an assertion about the
population distribution of one or more random
variables belonging to a particular population.
In other words statistical hypothesis is a state-
ment about the probability distribution of popu-
lation characteristics which are to be verified on
the basis of sample information. On the basis of
the amount of information provided by a hypoth-
esis, a statistical hypothesis is either (1)
9.2.1 Qualities of Good Hypothesis
1. Hypothesis should be clearly stated.
2. Hypothesis should be precise and stated in
simple form as far as possible.
3. Hypothesis should state the relationships
among the variables.
4. Hypothesis should be in the form of being
tested.
5. Hypothesis should be such that it can be tested
within the research area under purview.
Critical region
simple
or
(2)
composite
. Given a random variable from a
population, a
is a statistical
hypothesis which specifies all the parameters of
the probability distribution of the random vari-
able; otherwise it is a
simple hypothesis
. For
example, if we say that the height of the Indian
population is distributed normally with mean 5.6
0
and variance 15.6, then it is a simple hypothesis.
On the other hand, if we say that (1) the height of
the Indian population is distributed normally
with mean 5.6
0
or (2) the height of the Indian
population is distributed normally with variance
15.6 is composite in nature. Because to specify
the distribution of height which is distributed
normally, we require two information on mean
and variance of the population. Depending upon
the involvement or noninvolvement of the popu-
lation parameter in the statistical hypothesis, it is
again divided into
composite hypothesis
: Let a random sample
x
1
,
x
2
,
x
3
,
..., x
n
be represented by a point
x
in
n
-dimen-
sional sample space
being a subset of the
sample space, defined according to a prescribed
test such that it leads to the rejection of the null
hypothesis on the basis of the given sample if the
corresponding sample point
Ω
and
ω
x
falls in the subset
ω
ω
critical region
of
the test. As it rejects the null hypothesis, it is also
known as the
; the subset
is known as the
. The complemen-
tary region to the c
rit
ical region of the sample
space, that is,
ω
0
or
ω
,
is known as the
region of
acceptance
zone of rejection
. Two boundary values of the critical
region are also included in the region of
acceptance.
Errors in decision
nonparametric
hypothesis, and corresponding tests are either
parametric test or nonparametric test
parametric
or
. Thus, a
: In statistical inference,
drawing inference about the population parame-
ter based on sample observation may lead to the
following situations, and out of the four
situations in two situations, one can commit
errors. (Table
9.1
)
statistical hypothesis
μ ¼ μ
0
is a parametric
hypothesis, but testing whether a time series
data is random or not, that is, to test “the series
is random,” is a nonparametric hypothesis.
Any unbiased/unmotivated statistical asser-
tion (hypothesis) whose validity is to be tested
for possible rejection on the basis of sample
observations is called
9.2.2 Level of Significance
. And the
statistical hypothesis which contradicts the null
hypothesis is called the
null hypothesis
alternative hypothesis
.
The probability of committing type I error (
)is
called the level of significance. If the calculated
α
For
example,
against
the null hypothesis
